Volume of a Cylinder
In this lesson, we will learn about the volume of a cylinder.
About This Lesson
In this lesson, we will:
Learn how to derive the formula for the volume of a cylinder
See an example on using the formula to calculate the cylinder's volume
See an example on using the formula to calculate the height of a cylinder
below will explain more.
If we have a cylinder with the radius
, the volume,
of the cylinder is:
V = π
is a number that is approximately equals to 3.14.
The math video below will give more explanations about this formula. Also, we will see some examples on how to use it.
Math Video Transcript
00:00:03.060 In this lesson, we will learn about the volume of a cylinder. 00:00:07.090 Let’s start, consider this circle with the radius r. 00:00:12.040 By now, we should already know that the area, A, of this circle is pi r square. 00:00:18.080 Next, let's change this circle into a cylinder. 00:00:22.140 After doing so, this cylinder has the radius r, and the height h. 00:00:29.000 Now, to find the volume of this cylinder, V, we just multiply the area, A with the height, h. 00:00:38.100 Hence, we multiply pi r square, with h. 00:00:43.070 This gives the formula for the volume of a cylinder, V equal pi r square h. 00:00:51.080 Now, it is important that we include the unit for volume. 00:00:55.170 Since the unit is not given, we can write the unit as cubic unit. 00:01:01.210 Alright, let's see some examples on finding the volume of a cylinder. For these examples, we take pi as 3.14. 00:01:11.200 Find the volume of this cylinder which has the radius 3cm and the height 5cm. 00:01:18.140 Let's start by using the formula, V equal pi r square h. 00:01:24.040 Now, since the radius is given as 3 cm, we can substitute 'r' with 3. 00:01:31.140 Next, let's simplify 3 square. Here, we can see that 3 square equals to 3 multiply by 3. This gives 9. Let's write this down here. 00:01:46.180 Let's continue. The height h is given as 5 cm. Hence, we can substitute h with 5. 00:01:54.240 Now, we can simplify this equation by multiplying 9 with 5. This gives 45. 00:02:02.220 Next, pi is given as 3.14. So, let's substitute pi with 3.14. 00:02:12.140 Finally, we can find the volume by multiplying 3.14 with 45. This gives 141.30. 00:02:23.110 Note that, this number has no meaning unless we include the unit for it. 00:02:28.190 Since the radius and height are in centimeter, the volume will be in cubic centimeter. 00:02:34.200 Hence, the volume of this cylinder is 141.30 cubic centimeter. 00:02:42.130 Next example, the volume of this cylinder is 50 cubic ft and its radius is 2ft. Find its height, h. 00:02:51.180 Now, let's begin with the formula, V = pi r square h. 00:02:57.130 Since the volume of the cylinder is given as 50, we can substitute V with 50. 00:03:03.230 Next, since the radius is given as 2, we can substitute r with 2. 00:03:10.050 Now, let's simplify 2 square. 2 square is actually, 2 multiply by 2 which is equals to 4. Let's write this down here. 00:03:22.120 Next, we can substitute pi with 3.14. 00:03:27.120 Here, we can simplify this equation by multiplying 3.14 with 4. 00:03:33.120 This gives 12.56. 00:03:36.240 Now, we have 12.56 h equals to 50. Let's rewrite this equation so it will be easier to see. 00:03:46.230 Next, to solve for 'H', we divide both sides of the equation with 12.56. 00:03:54.140 This gives, h equals to, 50 divided by 12.56. 00:04:01.180 Now, we can find h by dividing 50 with 12.56. This gives 3.98. 00:04:10.180 Again, this number has no meaning unless we include the unit for it. 00:04:15.180 Since the radius is in feet, the height of the cylinder will also be in feet. 00:04:21.060 Hence, the height of the cylinder is 3.98 ft. 00:04:27.090 That is all for this lesson. Try out the practice question to test your understanding.
Practice Questions & More
Multiple Choice Questions (MCQ)
Now, let's try some MCQ questions to understand this lesson better.
You can start by going through the series of
questions on the volume of a cylinder
or pick your choice of question below.
on finding the volume of a cylinder
on finding the height of a cylinder
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